methods

Data Gathering and Preparation

Step 1: Locating the Spearhead

I went to Natural Resources Canada Mapping Services and searched for the Spearhead Range
I found that it was located at 92J02 on the NTS (National Topographic System) map.

Step 2: Finding a DEM

I searched the G: in the lab, and found the DEM for the appropriate area (92J02).

Step 3: Finding a Basemap

I needed a topo map with labels for all the geographic features. I found this at geogratis.ca
I downloaded a CanVec map, which apparently has better accuracy than NTS maps, but identifies everything in terms of coded shapefile names.
It was therefore necessary to compare the codes to a glossary in order to figure out what each feature is.

I removed all features that were extraneous to my analysis, such as transformers and other industrial features,
and I renamed all relevant features and turned relevant labels on. I then played around with color ramps, turned hillshading on to better represent the elevation changes, and began to create Map 1.
It was necessary to project the data (each piece individually, as ArcMap would not let me batch project) to a NAD1983 BC Environment Albers projection.

Step 4: Manually Drawing the Spearhead Route

It was necessary to represent the Spearhead Traverse on Map 1 as accurately as possible. A popular online guide book, trailpeak.com, provided the following information:
The Traverse

begins at the top of the Blackcomb Glacier, which is lift-accessed.
drops down to the Decker Glacier, staying low and heading SE.
Cross the northern glaciated slopes of Mt. Trorey. [Good camping can be found here.]
Mt. Pattison can be passed by the northern col or by climbing a short but steep west-facing chute south of the peak.
Cross high on the Tremor Glacier, and climb to a narrowing slot between Tremor and Shudder Mountains.
Head SE on high ground across the Platform Glacier [Good camping can be found here] to a col just west of Quiver Peak.
Traverse the upper western slopes of the Ripsaw Glacier, until you come to a keyhole on the glacier's southern edge.
Drop down from here onto the Naden Glacier, passing Mt. Macbeth on your right until you reach the top of the Macbeth Glacier, just north of Couloir Ridge.
Keeping to the skier's left, drop halfway down the glacier, passing a keyhole view of the Iago Glacier, to gain a south leading ridge.
Climb the ridge and follow it south until easier ground enables you to drop down onto the Iago Glacier.
Traverse the top of the Iago Glacier, and climb the eastern slopes of Mt Iago, until you can drop down onto the Diavolo Glacier.
Circumvent the southern slopes of Mt. Iago and Mt. Fitzsimmons, [passing good sites for camping.]
Veer westward and then decide between:

climbing the southern slope of Mt Benvolio onto the Benvolio Glacier, and climb the glacier to a point just east of Overlord.
alternatively, you can take a more direct but steeper route climbing onto the col between Mt. Fitzsimmons and Mt. Benvolio. Either way, this will get you to the top of the Fitzsimmons Glacier.

Stay on high ground, approaching Overlord Mountain from the east, passing north of a steep eastern spur off the peak of Overlord, and dropping down onto the Overlord Glacier a little down the cliffs SW of the main peak.
Traverse the upper slopes of the Overlord Glacier, [past good camping sites] and climb the mellow slopes west past Whirlwind Peak to a point just south of Fissile Peak and an unnamed bluff.
Head down this gentle valley towards Russet Lake, easily identifiable by a cabin on its northern banks.
Keeping to the high ground south of the Lake, climb Cowboy Ridge and drop down to the upper reaches of Melody Creek.
From this point you have two options:

follow the Singing Pass trail north down the western banks of Melody Creek, leading to a well-maintained trail above Fitzsimmons Creek, and then onto the lower slopes of the resort.
Alternatively, you can continue in a westerly direction to climb the slopes of the Musical Bumps, Oboe, Flute, and then Piccolo, giving you the entire vertical descent of Whistler ski resort to finish the day.

Step 5: Create Map 1 (Contour Map)

It was necessary to manually map the Spearhead Route. Luckily, the Route is not signposted, it is just an approximation and no two people are likely to do it the same if they are setting the skin track. Therefore, there are no problems regarding the accuracy of my traced route.
The contour map (Fig. 8) shows the topography in a manner in which the average map user is most familiar. I produced it in order that visitors to my site might better be able to visualize the terrain. However, elevation contours are too general for analysis, so it was necessary to produce a Digital Elevation Model (DEM) of the same area (Fig. 9).

The Spearhead Route

Contour Map		Digital Elevation Model

Fig. 8		Fig. 9

Click maps to enlarge

Considerations

Avalanche Danger Criteria

Slope:

The most avalanche-prone slopes are between 35 - 45 degrees, and within that range, the vast majority of human-triggered avalanches are on slopes between 38-40 degrees (Tremper 63).
Avalanche danger decreases both below and above the 35 - 45 degree range (Fig. 10).

Below that range, there is not as much stress exerted upon weak layers in the snowpack.
Above that range, slopes are steep enough to slide naturally (i.e. they 'self-control'), mitigating the risks of human-triggered avalanches.

Fig. 10

Image Courtesy of www.PisteHors.com

Aspect: Insolation

In midwinter when temperatures are low, cold snowpacks tend to develop more persistent weak layers than a warm snowpack.
North-facing slopes receive very little heat from the sun in midwinter (Fig. 11); East-facing slopes catch sun only in the morning when temps are colder (Fig. 12). South and West-facing slopes receive much more sun in higher temps. Therefore, the lion's share of avalanche accidents occur on North and East facing slopes. (Tremper 75)


Fig. 11		Fig. 12

Images courtesy of www.avalanche.org

This process is especially prevalent between 30 and 55 degrees (Fig. 13). The Spearhead Route falls within that range.

Fig. 13

Image courtesy of www.avalanche.org

Aspect: Windloading

Wind plays an important role in avalanche hazard. Wind can move a lot of snow very quickly, transforming a safe slope into a dangerous slope ten times as fast as snow falling from the sky (Tremper 81). It is an insidious process, because it is one that people tend to pay little attention to. Also, when the wind is blowing snow around, visibility declines - and with it, our perception of the world around us.
As the wind conveys the snow from one slope to another, the snow is ground into fine particles. Think of a snowflake; they generally have a number of fragile arms that break off in the turbulent process of being redistributed. When the wind slows down on the lee side of an obstacle, these finely-ground flakes consolidate into a heavy, dense layer that can overload persistent instabilities in the existing snowpack (Tremper 79).
Slopes can be loaded either from the top by wind-driven snow settling on the leeward side of a hill (Figs. 14, 15), or by a process of 'cross-loading,' where wind drives snow into protected pockets on the leeward side of ridges (Fig. 16).

Top-loading on leeward slopes	Top-loading on leeward slopes	Cross-loading on the leeward side of ridges

Fig. 14	Fig. 15	Fig. 16

Images courtesy of www.avalanche.org

Curvature/Terrain Variation

Safe travel in the backcountry often involves sticking to ridgelines (see Fig. 15, and Tremper 201). If an avalanche occurs, it is better to be above it than below. While this seems obvious, it is surprising how often it is overlooked.
A caveat: in particularly unstable conditions, avalanches can break high on a ridgeline, pulling you down with them. Also, some ridges offer little protection from powerful avalanches from above. Nonetheless, traveling on ridges is safer than traveling below them. The more prominent the ridge, the safer it is likely to be, especially if there is no hill above it.

Anisotropy

Slopes are, of course, anisotropic surfaces. That is, it requires more energy - there is more friction - to go up a hill than down it, especially on skis or a snowboard. Because no one would stick to a prescribed path that has them going up and over very steep hills instead of shallow gradients, it is important to include this in my least-cost analysis.

The Multi-Criteria Evaluation (MCE)

Standardization: I wanted to standardize all my criteria on a hazard scale of 1-100.

Slope:

I calculated the slope of the terrain from my DEM using the 'slope' tool in 3D Analyst.

I then converted it from a natural breaks scheme to a custom breaks scheme that reflected Bruce Tremper's table of 'Avalanches by Slope Steepness' on pg. 63. (as well as table 3-1 on the preceding page, where he mentions that slopes from 10-25 degrees can slide, though infrequently.)

In other words, I redefined the classifications according to delineations in level of avalanche hazard as defined by Bruce Tremper.

This custom scheme is represented on the map in Fig. 17

Avalanche Hazard with Respect to Slope:

Avalanche hazard with respect to slope is roughly on a bell-curve (Tremper 63).

I reclassified the Slope map using the 'Reclassify' tool to change the values from the slope classifications to a 'hazard' rating.

I calculated this hazard rating from the table by approximating from the graph how many incidences there were at each rating, and then dividing by 800 (although the graph describes 809 incidents, it is not rendered very precisely. I was forced to estimate all of the values. However, there is nothing to be gained from being precise here, because I am merely approximating a rating that reflects the relative hazard of each category).

0-10: base value (unadjusted)
10-25: base value (adjusted)
25-29: ~5/800 = .625
29-32: ~10/800 = 1.25
32-35: ~90/800 = 11.25
35-38: ~150/800 = 18.75
38-40: ~340/800 = 42.5
40-44: ~130/800 = 16.25
44-47: ~60/800 = 7.5
47-50: ~15/800 = 1.875
50-53: ~5/800 = .625
53-90: base value (adjusted)

Adjustments: I added a value of 50 to everything that Tremper gave a value in his graph. I assigned a value of 40 to both the 10-25 category and the 53-90 category to reflect that slides still occur here, but rarely. I assigned 0-10 a value of 1, because although weak layers in the snow can be present here, it is not steep enough to slide. (Fig. 18)

Slope (Degrees) In the Whistler Backcountry		Avalanche Hazard with Respect to Slope

Fig. 17		Fig. 18

Click to enlarge

Insolation:

I calculated aspect from my DEM using the Aspect tool in 3D Analyst. This is displayed in Fig. 19.
Aspect did not require manual reclassing because it was already in a convenient classification scheme for hazard analysis.
I used the reclassify tool to assign the following hazard ratings based on the information above (Figs. 11 - 13, Tremper 75) in addition to personal empirical observations of how aspects warm throughout the day.

Flat: 1
N: 90
NE: 90
E: 90
SE: 60
S: 30
SW: 30
W: 30
NW: 60
N: 90

Fig. 20 represents how insolation affects avalanche hazard on the terrain surrounding the Spearhead Route.

Aspect of Slopes In the Whistler Backcountry		Avalanche Hazard with Respect to Insolation

Fig. 19		Fig. 20

Click to enlarge

Windloading:

Fig. 21 below is identical to Fig. 11 above.

As mentioned aspect did not require manual reclassing because it was already in a convenient classification scheme for hazard analysis.
The prevailing wind in the Whistler area is from the south, according to the National Climate Data and Information Archive of Canada.
Combining that information with the knowledge of how snow is deposited over the terrain by wind (Figs. 14 - 16, Tremper 81), I estimated the following hazard ratings:

N: lee slope, greatest danger: 100

NW: crossloaded and toploaded (but not as dangerous as strict toploading, as some snow blows out onto the toploaded slopes): 87.5
W: crossloading, dangerous: 75
SW: catches some snow; danger present, but some snow still gets blown out. 25
S: windward slope, least danger. Tremper advises traveling on windward side of ridge: 1
SE: catches some snow; danger present, but some snow still gets blown out. 25
E: crossloading, dangerous: 75
NE: same as NW: 87.5
flat: no danger: 1

Aspect of Slopes In the Whistler Backcountry		Avalanche Hazard With Respect to Windloading

Fig. 21		Fig. 22

Click to enlarge

Curvature/Terrain Variation:

To find ridgelines, I calculated curvature from my DEM using the 'curvature' tool in 3D Analyst.

I manually reclassed (i.e. to a custom breaks scheme) the original raster, because I wanted to pick out the most prominent ridges. The natural breaks scheme lumped all the ridges from 3.5-12 together, and had lots of variation in the negative classes. I reclassed the positive values to 1-4, 4-8, and 8-12. This reclassification is represented in Fig. 23.
I then used the raster reclass tool and assigned hazard ratings as follows:

8 to12 = 1
4 to 8 = 5
1 to 4 = 10
0 to 1 = 50
-.5 to 0 = 60
-1 to -.5 = 70
-2 to -1 = 80
-9.7 to -2 = 90

These ratings reflect the fact that ridges (positive values) are safer than gullies (negative values), and that the more prominent the ridge, the safer it will generally be. The most prominent ridges are ridgetops that have no slopes above them. This is the safest travel route of all with respect to avalanche hazard (Fig. 15)
Avalanche hazard with respect to terrain variation is represented in Fig. 24.

Terrain Variation In the Whistler Backcountry		Avalanche Hazard With Respect to Terrain Variation

Fig. 23		Fig. 24

Click to enlarge

Weighting

I used an automated Analytical Hierarchy Calculator to determine weight.
Hierarchy is determined according to a subjective scale of importance (Fig. 25). User input defines the priority of each criterion over another, one at a time. This is known as a 'pairwise comparison.' The Analytical Hierarchy Calculator uses that input to assign each criterion a weight. For multi-criteria analyses, this removes some of the subjectivity of weighting by allowing direct comparison of each pair rather than a general comparison of all the criteria at once.



Fig. 25

Image courtesy of the Canadian Conservation Institute

Hierarchy

Curvature	3	Insolation
Curvature	6	Windloading
Curvature	-5	Slope
Insolation	6	Windloading
Insolation	1	Slope
Windloading	-6	Slope

Fig. 26

Weights

Curvature	28.3
Insolation	24.5
Windloading	4.52
Slope	42.5

Fig. 27

I then used the 'weighted sum' tool under spatial analyst to combine my criteria into one layer, my friction surface.
However, I realized upon looking at it that my analysis neglected a crucial criterion: terrain traps.

Fig. 28

Image courtesy of www.avalanche.org

Because I prioritized 'flat' areas within my slope, insolation, and wind-loading criteria, my curvature criteria was partially overridden. That is, although it successfully prioritized ridgelines, it did not have sufficient weight to render streambeds and rivers impassable. I checked this by turning on a 'stream' layer, and sure enough many of the areas of least-friction were along streambeds.

This is problematic because it recommends travel through areas that can become deeply filled with snow in the event of an avalanche (Fig. 28). It is not uncommon for avalanche victims to be buried 30 or more feet deep if they are caught in terrain traps. Retrieval from such deep burials is impossible. Body recovery efforts can be performed only in the spring when the snowpack melts.

To remedy this, I did two things:

Stream Layer

I put a 60m buffer on my stream layer, and then turned it into a raster.
I then used the reclass tool to give everything inside the buffer a friction value of 100 and ‘no data’ a friction value of zero.

Sinks

To ensure that I found all the depressions, I then used the hydrology tools to calculate Flow Direction, and used that to calculate Sinks, which are depressions in the landscape that may or may not be terrain traps.
Although some of these may be safe, there’s no point wasting energy going down and then back up for no gain, so it’s good to eliminate them anyway.
This layer was already a raster, so I used the reclassify tool to give all data a friction value of 100 and ‘no data’ a friction value of zero.

Once this was done, I used the raster calculator to add them together into a single layer, 'Terrain Traps.'

Because there was some overlap, it was necessary to again use the reclassify tool to normalize the data to a friction value of 100.

I was then able to reproduce my weights with the terrain trap layer included (Fig. 30). I revised my opinion of my hierarchy assignments from the first time (Fig. 26), deciding to factor in the respective accuracy of each criterion as well as its significance to avalanche hazard (Fig. 29).

Hierarchy

Curvature	-3	Insolation
Curvature	1	Windloading
Curvature	-3	Slope
Curvature	1	Terrain Traps
Insolation	6	Windloading
Insolation	1	Slope
Insolation	3	Terrain Traps
Windloading	-6	Slope
Windloading	-3	Terrain Traps
Slope	3	Terrain Traps

Fig. 29

Weights

Curvature	10.5
Insolation	35.04
Windloading	6.55
Slope	35.04
Terrain Traps	12.86

Fig. 30

I then used the 'weighted sum' tool to produce my final friction surface layer (Fig. 31).

My inputs were the 5 normalized criteria
I used the results of the Analytical Hierarchy Process to weight them.
The product is the result of my MCE. It represents avalanche hazard in the terrain surrounding the Spearhead Route as influenced by my selected criteria. Each cell has a certain hazard value that represents the combination of the hazard values of each criterion.

Avalanche Hazard On the Spearhead Route
As Influenced by Slope, Insolation, Windloading,
Terrain Variation and Terrain Traps

Fig. 31

Click to enlarge

Jump to Results

The Least-Cost Path

The Spearhead Route

'Cost', in this case, represents hazard. A cell with a high cost or friction value represents an area that is more hazardous to travel through with respect to avalanche danger than a cell with low cost.
Because I wanted my least-cost path to follow the Spearhead Route, it was necessary to include waypoints. Otherwise, the least-cost path would likely go directly from Blackcomb to Whistler without circumventing the Spearhead Range.
Conveniently, the Route is often done as a multiday trip, although skilled backcountry guides have done it in as little as eight hours. There are areas along the way that are recommended for camping. I selected my sites based upon the recommendations from trailpeak.com. I further specified the locations using the information provided by my MCE. All of the campsites (Camps 1-4) are located in 'safe' areas of the map. I used the Whistler and Blackcomb boundaries as start and end points, because within resort boundaries conditions are controlled, and any path down either mountain is more or less equal with respect to avalanche hazard.

Anisotropy

It is necessary for my analysis to reflect that mountains are an anisotropic surface. Recall that slope is on a bell curve. Because steeper slopes are often just as safe with respect to avalanche danger as low-angle slopes, the calculated least-cost path might go up impassably steep slopes, or at least consistently favor slopes above 45 degrees.
ArcGIS makes a provision for anisotropic surfaces by allowing you to calculate 'Path Distance.' Path Distance calculates for each cell the least accumulative cost distance to the nearest source, while accounting for horizontal and vertical factors.
Therefore, part of the 'cost' of each cell is the difficulty of travelling through it based on whether you are climbing or descending.

Path Distance

The path distance (or cost distance for isotropic surfaces) is a necessary input for a least-cost path calculation.
To compute the path distance, I used the following inputs:

Feature source: Blackcomb_bound (the Blackcomb resort boundary)

The feature source is the location to which the least accumulated cost distance for every cell is calculated.

Input cost raster: MCEOutput2 (the result of my revised MCE including terrain traps)

Defines the impedance of moving through each cell while compensating for diagonal movement.
This is important, because squares are longer on their diagonals than their sides.

Input surface raster: proj_DEM

This defines the elevation for each cell to calculate the actual surface distance that will be covered when passing between cells.

Input vertical raster: proj_DEM

Defines the z-values for each cell location and calculates the slope to identify the vertical factor incurred when moving from one cell to another.

It was necessary to ensure that the environment settings matched my map settings.
I then computed path distances (and backlink rasters) for Camps 1 - 4 as well.

The only input that changed between operations was the feature source.

Cost Path

To compute the cost path, I used the following inputs:

Feature destination: Camp 1

This is the location to which the path is calculated.

Input cost distance raster: Pdist_b_b (my path distance output from the Blackcomb boundary location)

This is the information used to determine the least-cost path.

Input cost backlink raster: bb_backlink (my backlink output from the Blackcomb boundary location)

This is used to determine the path to return to a source via the least-cost path.

Path type: BEST_SINGLE

This ensures that the least-cost path is derived from the cell with the minimum of least-cost paths to source cells.
That is, it selects the path from one cell to another based upon which of the adjacent cells has the best option (least impedance) among its own adjacent cells.

Again, it was necessary to ensure that the environment settings matched my map settings.
I computed Cost Paths through each of my points:

Blackcomb boundary to Camp 1
Camp 1 to Camp 2
Camp 2 to Camp 3
Camp 3 to Camp 4
Camp 4 to Whistler boundary.

The result was a continuous least-cost path that follows the Spearhead Route.

Back to Introduction - Continue to Results